Boundary Value Problems
Volume 2007 (2007), Article ID 16407, 8 pages
doi:10.1155/2007/16407

Entire bounded solutions for a class of quasilinear elliptic equations

Abstract

We consider the problem −div(|∇u|p−2∇u)=a(x)(um+λun), x∈ℝN, N≥3, where 0<m<p−1<n,a(x)≥0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists λ0>0 such that the above-mentioned equation admits at least one solution for all λ∈(0,λ0). This extends the results of Laplace equation to the case of p-Laplace equation.